21127 Lecture Notes - Lecture 11: European Route E6, Contraposition, Exclusive Economic Zone
16 Dec 2015
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The phrase if and only if means exactly that: if and only if. P if q clearly means if q then p , i. e. q p . P only if q means it cannot be the case that p holds and q fails . That is, the only case where p q fails is false. P q is logically the same as saying p q q p. We will use to assert that two statements are logically equivalent. Remember, = applies to numbers or sets only! The symbol applies to two statements with truth values. We use in de nitions to say that some concept is logically equivalent to its de nition. For example, we would de ne even by saying. Given any x z we say x is even k z. x = 2k. We also use to say two statements are logically equivalent, that they have the same truth value, whatever value that might be.
